Sparse QRAM Enables Resource-Efficient Quantum Convolutional Operations

Convolution, a fundamental operation in image processing and deep learning, presents a significant challenge when translated to quantum computing due to its inherent complexity and data requirements. Mohammad Rasoul Roshanshah, Payman Kazemikhah, and Hossein Aghababa, from their respective institutions, now demonstrate a resource-efficient quantum algorithm that reformulates convolution as a structured matrix multiplication, dramatically reducing computational costs. The team achieves this by cleverly encoding convolutional data as sparse matrices and representing filters in superposition, allowing for efficient computation through a streamlined inner product estimation process. This innovative approach eliminates unnecessary data preparation, scales favourably with input size, and importantly, paves the way for integrating quantum computation into practical, hybrid machine learning systems, potentially revolutionising feature extraction and data-driven inference.

Sparse Tensor Convolution on Quantum Computers

This research proposes a novel quantum algorithm for performing convolutional operations, a core component of deep learning, within Convolutional Neural Networks (CNNs). The authors address the challenge of efficiently implementing these operations on quantum computers, which traditionally struggle with large data volumes and complex computations. The method leverages sparsity in convolutional filters and feature maps, representing only non-zero elements to reduce qubit and gate requirements. Convolutional filters are represented as quantum states in superposition, allowing for efficient processing, and outputs are computed through inner product estimation using a low-depth SWAP test circuit with reduced sampling overhead.

Quantum Convolution via Sparse Matrix Multiplication

Researchers have developed a new method for performing convolution, a fundamental operation in image processing and machine learning, using quantum computing. This approach reformulates convolution as a sparse matrix multiplication to overcome limitations of existing methods. By leveraging sparsity, the researchers minimize the resources needed to represent images and filters as quantum states. This sparse encoding, combined with a specialized state preparation technique, reduces computational complexity, and the method utilizes a quantum circuit called the SWAP test to estimate inner products with lower circuit depth than previously possible.

Quantum Convolution via Sparse Matrix Encoding

This work introduces a new quantum algorithm for accelerating convolution operations, a fundamental process in image processing and machine learning. By reformulating convolution as a sparse matrix multiplication, the researchers demonstrate a reduction in computational cost and a pathway towards more efficient quantum feature extraction. The method efficiently encodes input data and convolutional filters into quantum states, avoiding the redundancies required by previous approaches, and output is estimated using low-depth quantum circuits for scalable implementation.

This algorithm’s design prioritizes compatibility with existing quantum memory architectures and offers adaptability to various convolutional parameters. The researchers highlight that future work should focus on hardware-aware optimizations to reduce circuit depth and improve performance on current noisy quantum devices, especially for large-batch convolution tasks. Further integration of this quantum convolution framework into broader machine learning models could create efficient quantum preprocessing layers within deep neural networks. The results demonstrate a substantial improvement in computational efficiency, particularly for large images and filters, and the method scales logarithmically with input size under sparsity, meaning the computational cost grows much more slowly as image or filter size increases.